FRM Part II · FRM Exam Part II · Portfolio Risk: Analytical Methods
An investor has two uncorrelated assets with expected excess returns of 4% and 6% and volatilities of 10% and 20%. Under mean-variance optimization with uncorrelated assets, the optimal weights are proportional to expected excess return divided by variance. What is the ratio of the optimal weight in Asset 2 to the weight in Asset 1?
The ratio is 0.375. With uncorrelated assets, optimal weights are proportional to excess return over variance: 4 for Asset 1 and 1.5 for Asset 2, so Asset 2's weight is 0.375 times Asset 1's.
- A0.375Correct
- B1.5
- C0.60
- D2.67
Explanation
Weight is proportional to mu/sigma^2. Asset 1: 0.04/0.01 = 4. Asset 2: 0.06/0.04 = 1.5. Ratio = 1.5/4 = 0.375. Using 1.5 ignores the variance of Asset 1; 0.60 divides returns by volatility rather than variance.
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